Capillary phenomena in the framework of the two-dimensional density functional theory

We present results of application of the density functional theory (DFT) to adsorption and desorption in finite and infinite cylindrical pores accounting for the density distribution in radial and axial directions. Capillary condensation via formation of bridges is considered using canonical and grand canonical versions of the 2D DFT. The potential barrier of nucleation is determined as a function of the bulk pressure and the pore diameter. In the framework of the conventional assumptions on intermolecular interactions both 1D and 2D DFT versions lead to the same results and confirm the classical scenario of condensation and evaporation: the condensation occurs at the vapor-like spinodal point, and the evaporation corresponds to the equilibrium transition pressure. The analysis of experimental data on argon and nitrogen adsorption on MCM-41 samples seems to not completely corroborate this scenario, with adsorption branch being better described by the equilibrium pressure - diameter dependence. This points to the necessity of the further development of basic representations on the hysteresis phenomena.

Pore size characterization of mesoporous materials by a thermodynamic approach: A curvature-dependent solid-fluid potential

A thermodynamic analysis of nitrogen adsorption in cylindrical pores of MCM-41 and SBA-15 samples at 77 K is presented within the framework of the Broekhoff and de Boer (BdB) theory. We accounted for the effect of the solid surface curvature on the potential exerted by the pore walls. The developed model is in quantitative agreement with the non-local density functional theory (NLDFT) for pores larger than 2 tun. This modified BdB theory accounting for the Curvature Dependent Potential (CDP-BdB) was applied to determine the pore size distribution (PSD) of a number of MCM-41 and SBA-15 samples on the basis of matching the equilibrium theoretical isotherm against the adsorption branch of the experimental isotherm. In all cases investigated the PSDs determined with the new approach are very similar to those determined with the non-local density functional theory also using the same basis of matching of theoretical isotherm against the experimental adsorption branch. The developed continuum theory is very simple in its utilization, suggesting that CDP-BdB could be used as an alternative tool to obtain PSD for mesoporous solids from the analysis of adsorption branch of adsorption isotherms of any sub-critical fluids.

Improvement of the Derjaguin-Broekhoff-de Boer theory for capillary condensation/evaporation of nitrogen in mesoporous systems and its implications for pore size analysis of MCM-41 silicas and related materials

In this work, we propose an improvement of the classical Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in mesoporous systems. The primary idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the surface tension changes in mesopores. In addition, the statistical film thickness (so-called t-curve) evaluated accurately on the basis of the adsorption isotherms measured for the MCM-41 materials is used instead of the originally proposed t-curve (to take into account the excess of the chemical potential due to the surface forces). It is shown that the aforementioned modifications of the original DBdB theory have significant implications for the pore size analysis of mesoporous solids. To verify our improvement of the DBdB pore size analysis method (IDBdB), a series of the calcined MCM-41 samples, which are well-defined materials with hexagonally ordered cylindrical mesopores, were used for the evaluation of the pore size distributions. The correlation of the IDBdB method with the empirically calibrated Kruk-Jaroniec-Sayari (KJS) relationship is very good in the range of small mesopores. So, a major advantage of the IDBdB method is its applicability for small mesopores as well as for the mesopore range beyond that established by the KJS calibration, i.e., for mesopore radii greater than similar to4.5 nm. The comparison of the IDBdB results with experimental data reported by Kruk and Jaroniec for capillary condensation/evaporation as well as with the results from nonlocal density functional theory developed by Neimark et al. clearly justifies our approach. Note that the proposed improvement of the classical DBdB method preserves its original simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the mean pore size by the powder X-ray diffraction method.

Application of a generalized thermodynamic approach to characterize mesoporous materials

Equilibrium adsorption and desorption in mesoporous adsorbents is considered on the basis of rigorous thermodynamic analysis, in which the curvature-dependent solid-fluid potential and the compressibility of the adsorbed phase are accounted for. The compressibility of the adsorbed phase is considered for the first time in the literature in the framework of a rigorous thermodynamic approach. Our model is a further development of continuum thermodynamic approaches proposed by Derjaguin and Broekhoff and de Boer, and it is based on a reference isotherm of a non-porous material having the same chemical structure as that of the pore wall. In this improved thermodynamic model, we incorporated a prescription for transforming the solid-fluid potential exerted by the flat reference surface to the potential inside cylindrical and spherical pores. We relax the assumption that the adsorbed film density is constant and equal to that of the saturated liquid. Instead, the density of the adsorbed fluid is allowed to vary over the adsorbed film thickness and is calculated by an equation of state. As a result, the model is capable to describe the adsorption-desorption reversibility in cylindrical pores having diameter less than 2 nm. The generalized thermodynamic model may be applied to the pore size characterization of mesoporous materials instead of much more time-consuming molecular approaches. (c) 2005 Elsevier B.V. All rights reserved.

Comparison of nitrogen adsorption at 77 K on non-porous silica and pore wall of MCM-41 materials by means of density functional theory

Nitrogen adsorption on a surface of a non-porous reference material is widely used in the characterization. Traditionally, the enhancement of solid-fluid potential in a porous solid is accounted for by incorporating the surface curvature into the solid-fluid Potential of the flat reference surface. However, this calculation procedure has not been justified experimentally. In this paper, we derive the solid-fluid potential of mesoporous MCM-41 solid by using solely the adsorption isotherm of that solid. This solid-fluid potential is then compared with that of the non-porous reference surface. In derivation of the solid-fluid potential for both reference surface and mesoporous MCM-41 silica (diameter ranging front 3 to 6.5 nm) we employ the nonlocal density functional theory developed for amorphous solids. It is found that, to out, surprise, the solid-fluid potential of a porous solid is practically the same as that for the reference surface, indicating that there is no enhancement due to Surface curvature. This requires further investigations to explain this unusual departure from our conventional wisdom of curvature-induced enhancement. Accepting the curvature-independent solid-fluid potential derived from the non-porous reference surface, we analyze the hysteresis features of a series of MCM-41 samples. (c) 2005 Elsevier Inc. All rights reserved.

Pore size distribution analysis of activated carbons: Application of density functional theory using nongraphitized carbon black as a reference system

The application of nonlocal density functional theory (NLDFT) to determine pore size distribution (PSD) of activated carbons using a nongraphitized carbon black, instead of graphitized thermal carbon black, as a reference system is explored. We show that in this case nitrogen and argon adsorption isotherms in activated carbons are precisely correlated by the theory, and such an excellent correlation would never be possible if the pore wall surface was assumed to be identical to that of graphitized carbon black. It suggests that pore wall surfaces of activated carbon are closer to that of amorphous solids because of defects of crystalline lattice, finite pore length, and the presence of active centers.. etc. Application of the NLDFT adapted to amorphous solids resulted in quantitative description of N-2 and Ar adsorption isotherms on nongraphitized carbon black BP280 at their respective boiling points. In the present paper we determined solid-fluid potentials from experimental adsorption isotherms on nongraphitized carbon black and subsequently used those potentials to model adsorption in slit pores and generate a corresponding set of local isotherms, which we used to determine the PSD functions of different activated carbons. (c) 2005 Elsevier Ltd. All rights reserved.

Osmotic flow in porous membranes:effects of electric charge

The electrostatic model for osmotic flow across a porous membrane in our previous study (Akinaga et al. 2008)" was extended to include the streaming potential, for solutes and pores of like charge and fixed surface charge densities. The magnitude of the streaming potential was determined to satisfy zero current condition along the pore axis. It was found that the streaming potential affects the velocity profiles of the pressure driven flow as well as the osmotic flow through the pore, and decreases their flow rates, particularly in the case of large Debye length relative to the pore radius, whereas it has little effect on the reflection coefficients of spherical solutes through cylindrical pores.

Charge effects on hindrance factors for diffusion and convection of solute in pores I

The transport of a spherical solute through a long circular cylindrical pore filled with an electrolyte solution is studied numerically, in the presence of constant surface charge on the solute and the pore wall. Fluid dynamic analyses were carried out to calculate the flow field around the solute in the pore to evaluate the drag coefficients exerted on the solute. Electrical potentials around the solute in the electrolyte solution were computed based on a mean-field theory to provide the interaction energy between the charged solute and the pore wall. Combining the results of the fluid dynamic and electrostatic analyses, we estimated the rate of the diffusive and convective transport of the solute across the pore. Although the present estimates of the drag coefficients on the solute suggest more than 10% difference from existing studies, depending on the radius ratio of the solute relative to the pore and the radial position of the solute center in the pore, this difference leads to a minor effect on the hindrance factors. It was found that even at rather large ion concentrations, the repulsive electrostatic interaction between the charged solute and the pore wall of like charge could significantly reduce the transport rate of the solute.

A quasi stationary approach to drying kinetics of cylindrical food particulates in a heat pump asisted fluid bed dryer

Experiments were undertaken to study drying kinetics of moist cylindrical shaped food particulates during fluidised bed drying. Cylindrical particles were prepared from Green beans with three different length:diameter ratios, 3:1, 2:1 and 1:1. A batch fluidised bed dryer connected to a heat pump system was used for the experimentation. A Heat pump and fluid bed combination was used to increase overall energy efficiency and achieve higher drying rates. Drying kinetics, were evaluated with non-dimensional moisture at three different drying temperatures of 30, 40 and 50o C. Numerous mathematical models can be used to calculate drying kinetics ranging from analytical models with simplified assumptions to empirical models built by regression using experimental data. Empirical models are commonly used for various food materials due to their simpler approach. However problems in accuracy, limits the applications of empirical models. Some limitations of empirical models could be reduced by using semi-empirical models based on heat and mass transfer of the drying operation. One such method is the quasi-stationary approach. In this study, a modified quasi-stationary approach was used to model drying kinetics of the cylindrical food particles at three drying temperatures.

Defining the flammability of cylindrical metal rods through characterization of the thermal effects of the ignition promoter

All relevant international standards for determining if a metallic rod is flammable in oxygen utilize some form of “promoted ignition” test. In this test, for a given pressure, an overwhelming ignition source is coupled to the end of the test sample and the designation flammable or nonflammable is based upon the amount burned, that is, a burn criteria. It is documented that (1) the initial temperature of the test sample affects the burning of the test sample both (a) in regards to the pressure at which the sample will support burning (threshold pressure) and (b) the rate at which the sample is melted (regression rate of the melting interface); and, (2) the igniter used affects the test sample by heating it adjacent to the igniter as ignition occurs. Together, these facts make it necessary to ensure, if a metallic material is to be considered flammable at the conditions tested, that the burn criteria will exclude any region of the test sample that may have undergone preheating during the ignition process. A two-dimensional theoretical model was developed to describe the transient heat transfer occurring and resultant temperatures produced within this system. Several metals (copper, aluminum, iron, and stainless steel) and ignition promoters (magnesium, aluminum, and Pyrofuze®) were evaluated for a range of oxygen pressures between 0.69 MPa (100 psia) and 34.5 MPa (5,000 psia). A MATLAB® program was utilized to solve the developed model that was validated against (1) a published solution for a similar system and (2) against experimental data obtained during actual tests at the National Aeronautics and Space Administration White Sands Test Facility. The validated model successfully predicts temperatures within the test samples with agreement between model and experiment increasing as test pressure increases and/or distance from the promoter increases. Oxygen pressure and test sample thermal diffusivity were shown to have the largest effect on the results. In all cases evaluated, there is no significant preheating (above about 38°C/100°F) occurring at distances greater than 30 mm (1.18 in.) during the time the ignition source is attached to the test sample. This validates a distance of 30 mm (1.18 in.) above the ignition promoter as a burn length upon which a definition of flammable can be based for inclusion in relevant international standards (that is, burning past this length will always be independent of the ignition event for the ignition promoters considered here. KEYWORDS: promoted ignition, metal combustion, heat conduction, thin fin, promoted combustion, burn length, burn criteria, flammability, igniter effects, heat affected zone.

The rate-limiting mechanism for the heterogeneous burning of cylindrical iron rods

This paper presents the findings of an investigation into the rate-limiting mechanism for the heterogeneous burning in oxygen under normal gravity and microgravity of cylindrical iron rods. The original objective of the work was to determine why the observed melting rate for burning 3.2-mm diameter iron rods is significantly higher in microgravity than in normal gravity. This work, however, also provided fundamental insight into the rate-limiting mechanism for heterogeneous burning. The paper includes a summary of normal-gravity and microgravity experimental results, heat transfer analysis and post-test microanalysis of quenched samples. These results are then used to show that heat transfer across the solid/liquid interface is the rate-limiting mechanism for melting and burning, limited by the interfacial surface area between the molten drop and solid rod. In normal gravity, the work improves the understanding of trends reported during standard flammability testing for metallic materials, such as variations in melting rates between test specimens with the same cross-sectional area but different crosssectional shape. The work also provides insight into the effects of configuration and orientation, leading to an improved application of standard test results in the design of oxygen system components. For microgravity applications, the work enables the development of improved methods for lower cost metallic material flammability testing programs. In these ways, the work provides fundamental insight into the heterogeneous burning process and contributes to improved fire safety for oxygen systems in applications involving both normal-gravity and microgravity environments.

Characteristics of modal sound radiation of finite cylindrical shells

Characteristics of modal sound radiation of finite cylindrical shells are studied using finite element and boundary element methods in this paper. In the low frequency range, modal radiation efficiencies of finite cylindrical shells are found to asymptotically approach those of the corresponding infinite cylindrical shell when structural trace wavelengths of the cylindrical shells are greater than the acoustic wavelength. Modal radiation efficiencies for each group of modes having the same circumferential modal index decrease as the axial modal index increases. They converge to each other when the axial trace wavelength is much greater than the circumferential trace wavelength. The mechanism leading to lower radiation efficiency of modes with higher circumferential modal index of short cylinders is explained. Similar to those of flat plate panels, change in slope or waviness is observed in modal radiation efficiency curves of modes with higher order axial modal index at medium frequencies. This is attributed to the interference of sound radiated by neighbouring vibrating cells when the distance between nodal lines of a vibrating mode is in the same order or smaller than the acoustic wavelength. Effects of the internal sound field on modal radiation efficiencies of a finite open-end cylinder are discussed.

Preparation and characterisation of tri-calcium phosphate scaffolds with tunnel-like macro-pores for bone tissue engineering

Calcium Phosphate ceramics have been widely used in tissue engineering due to their excellent biocompatibility and biodegradability. In the physiological environment, they are able to gradually degrade, absorbed and promote bone growth. Ultimately, they are capable of replacing damaged bone with new tissue. However, their low mechanical properties limit calcium phosphate ceramics in load-bearing applications. To obtain sufficient mechanical properties as well as high biocompatibility is one of the main focuses in biomaterials research. Therefore, the current project focuses on the preparation and characterization of porous tri-calcium phosphate (TCP) ceramic scaffolds. Hydroxapatite (HA) was used as the raw material, and normal calcium phosphate bioglass was added to adjust the ratio between calcium and phosphate. It was found that when 20% bioglass was added to HA and sintered at 1400oC for 3 hours, the TCP scaffold was obtained and this was confirmed by X-ray diffraction (XRD) analysis. Test results have shown that by applying this method, TCP scaffolds have significantly higher compressive strength (9.98MPa) than those made via TCP powder (<3MPa). Moreover, in order to further increase the compressive strength of TCP scaffolds, the samples were then coated with bioglass. For normal bioglass coated TCP scaffold, compressive strength was 16.69±0.5MPa; the compressive strength for single layer mesoporous bioglass coated scaffolds was 15.03±0.63MPa. In addition, this project has also concentrated on sizes and shapes effects; it was found that the cylinder scaffolds have more mechanical property than the club ones. In addition, this project performed cell culture within scaffold to assess biocompatibility. The cells were well distributed in the scaffold, and the cytotoxicity test was performed by 3-(4,5)-dimethylthiahiazo(-z-y1)-3,5-di- phenytetrazoliumromide (MTT) assay. The Alkaline Phosphatase (Alp) activity of human bone marrow mesenchymal stem cell system (hBMSCs) seeded on scaffold expressed higher in vitro than that in the positive control groups in osteogenic medium, which indicated that the scaffolds were both osteoconductive and osteoinductive, showing potential value in bone tissue engineering.